Related papers: Planar Projections and Second Intrinsic Volume
Rare events of large-scale spatially-correlated exponential random fields are studied. The influence of spatial correlations on clustering and non-sphericity is investigated. The size of the performed simulations permits to study…
The present paper considers volume formulae, as well as trigonometric identities, that hold for a tetrahedron in 3-dimensional spherical space of constant sectional curvature +1. The tetrahedron possesses a certain symmetry: namely rotation…
We collect a few guesses on possible implications of a lower bound on the scalar curvature of a Riemannian manifold on the size and shape of this manifold.
This note conducts a comparative study of some approximating properties of the metric projection, generalized projection, and generalized metric projection in uniformly convex and uniformly smooth Banach spaces. We prove that the inverse…
Averaging in general relativity is a complicated operation, due to the general covariance of the theory and the non-linearity of Einstein's equations. The latter of these ensures that smoothing spacetime over cosmological scales does not…
The ubiquity of optical coherence arising from its importance in everything from astronomy to photovoltaics means that underlying assumptions such as stationarity and ergodicity can become implicit. When these assumptions become implicit,…
The note describes the cones in the Euclidean space admitting isotonic metric projection with respect to the coordinate-wise ordering. As a consequence it is showed that the metric projection onto the regression cone (the cone defined by…
For n >= 2 a construction is given for a large family of compact convex sets K and L in n-dimensional Euclidean space such that the orthogonal projection L_u onto the subspace u^\perp contains a translate of the corresponding projection K_u…
Different extended objects can fall in different ways, depending on their internal structures. Some motions are nevertheless impossible, regardless of internal structure. This paper derives universal constraints on extended-body motion,…
Frustrated total internal reflection is analyzed from an unusual point of view Unlike most similar works, incident angles are used here as the scanning variable, instead of the tunneled film thickness. The theoretical framework is presented…
Previous studies on the geometrical properties of the state space of a finite-level quantum system have determined its volume and surface area. Building on this foundation, we derive explicit formulas for two additional intrinsic volume…
We explore the shadow of certain class generalized Kerr black holes, which are non vacuum solutions of the Einstein equations with exotic matter. The images depend on the angular momentum of the compact object, the characteristic parameter…
Deriving the 3-dimensional volume density distribution from a 2-dimensional light distribution of a system yields generally non-unique results. The case for nearby dust-free systems is studied, taking into account the extra constraints from…
We study the nonexpansivity of reflection mappings in geodesic spaces and apply our findings to the averaged alternating reflection algorithm employed in solving the convex feasibility problem for two sets in a nonlinear context. We show…
We explore the phenomenological implications of generalizing measures to a multidimensional multiverse. We consider a simple model in which the vacua are nucleated from a $D$-dimensional parent spacetime through dynamical compactification…
The volume of a Meissner polyhedron is computed in terms of the lengths of its dual edges. This allows to reformulate the Meissner conjecture regarding constant width bodies with minimal volume as a series of explicit finite dimensional…
The class of norm-dependent Random Matrix Ensembles is studied in the presence of an external field. The probability density in those ensembles depends on the trace of the squared random matrices, but is otherwise arbitrary. An exact…
We study the relationship between the ratio of intrinsic to extrinsic metrics and area. For certain surfaces inside unit ball in R3 we give lower bound on the maximum of ratio in terms of its area. We also give examples to show…
Analytic relations are derived for finite volume integrals over the radial distribution function of a fluid, so-called Kirkwood-Buff integrals. Closed form expressions are obtained for cubes and cuboids, the system shapes commonly employed…
It is proved that the projection constants of two- and three-dimensional spaces are bounded by $4/3$ and $(1+\sqrt 5)/2$, respectively. These bounds are attained precisely by the spaces whose unit balls are the regular hexagon and…